Investigating foul balls as a skill

From SABR member Bill Petti at Beyond the Box Score on November 10, 2011:

It's often said that good hitters have an ability to protect the plate and extend at-bats by fouling off pitches. We've all heard some version of this, typically during broadcasts and almost certainly during sequences where a hitter manages to work a pitcher by fouling off a large number of pitches.

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I decided to update things a bit, looking at batter data from 2008 to 2011 for hitters with >250 plate appearances in each season.

Here's what I found:

The Year-to-Year correlation of Foul Ball Percentage (FB%)* was .72, which is pretty good when we think about hitting statistics.** It suggests, like [Russell Carleton]'s study, that the ability to hit foul balls is a skill or talent that hitters generally replicate season to season.

The ability to hit foul balls does not necessarily indicate that a hitter is more skilled. The correlation with Weighted On-Base Average (wOBA), while positive, was only .23. Similarly, the ability to get on base (OBP) had next to no relationship with FB% (.079). The one batted ball outcome that did show the strongest correlation was power. Isolated power (ISO) managed to correlate at .45 and HR/FB at .47. This makes sense as strikeouts showed the strongest overall relationship (.74) and we know that hitters that display greater power tend to have higher strikeout rates.